Problem 6.3¶

Importing packages¶

In [ ]:
import numpy as np
from sklearn.svm import SVR
from sklearn import svm
from sklearn.metrics.pairwise import linear_kernel, polynomial_kernel, rbf_kernel
from sklearn.metrics import mean_squared_error
import matplotlib.pyplot as plt

1) Construct a train dataset and represent them.¶

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def data(N,a):
   N=N+3
   h=np.array([1,a])
   y=np.sign(np.random.randn(N,1))
   y=np.reshape(y,len(y))
   t=np.arange(N)
   z=np.convolve(h,y)
   z=z[1:N-1]
   y=y[2:N-1]
   X=np.array([z[0:N-3],z[1:N-2]])+0.2*np.random.randn(2,N-3)
   return X,y


data_alpha = 1.5  # Parameter 'a' for data generation
N_train = 100  # Number of training samples
X_train, y_train = data(N_train, data_alpha)

N_Val = 110  # Number of validation samples
X_Val, y_Val = data(N_Val, data_alpha)

N_test = 1000  # Number of test samples
X_test, y_test = data(N_test, data_alpha)

print("Shape of X_train: ", X_train.shape)
print("Shape of y_train: ", y_train.shape)
print("Shape of X_Val: ", X_Val.shape)
print("Shape of y_Val: ", y_Val.shape)
print("Shape of X_test: ", X_test.shape)
print("Shape of y_test: ", y_test.shape)


plt.figure(figsize=(15, 5))

plt.subplot(131)
ind1=np.where(y_train==1)
ind2=np.where(y_train==-1)
plt.plot(X_train[0,ind1],X_train[1,ind1],'b*')
plt.plot(X_train[0,ind2],X_train[1,ind2],'r*')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Training Data')

plt.subplot(132)
ind1=np.where(y_test==1)
ind2=np.where(y_test==-1)
plt.plot(X_test[0,ind1],X_test[1,ind1],'b*')
plt.plot(X_test[0,ind2],X_test[1,ind2],'r*')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Test Data')

plt.subplot(133)
ind1=np.where(y_Val==1)
ind2=np.where(y_Val==-1)
plt.plot(X_Val[0,ind1],X_Val[1,ind1],'b*')
plt.plot(X_Val[0,ind2],X_Val[1,ind2],'r*')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Validation Data')

plt.tight_layout()
plt.show()
Shape of X_train:  (2, 100)
Shape of y_train:  (100,)
Shape of X_Val:  (2, 110)
Shape of y_Val:  (110,)
Shape of X_test:  (2, 1000)
Shape of y_test:  (1000,)
No description has been provided for this image

Linear Kernel¶

In [ ]:
# Computing kernel matrices
K_linear = linear_kernel(X_train.T, X_train.T)
C_high = 5; C_low = -5
C_Values = np.logspace(C_low, C_high, C_high - C_low + 1, base=10)

MMSE_linear = np.zeros(len(C_Values))
total_iterations = len(C_Values)

# Train SVM with precomputed kernel matrices
for i, C in enumerate(C_Values):
    clf_linear = svm.SVC(kernel='precomputed', C=C)

    # Fit the model
    clf_linear.fit(K_linear, y_train)

    # Validation set
    K_val_linear = linear_kernel(X_Val.T, X_train.T)

    # Predict on validation set
    y_pred_linear = clf_linear.predict(K_val_linear)
    
    # Compute validation error
    val_error_linear = np.mean(y_pred_linear != y_Val)
    # MMSE_linear[i] = mean_squared_error(y_Val, y_pred_linear)
    MMSE_linear[i] = np.mean((y_pred_linear - y_Val)**2)

    # % Complete status update
    print("Completed ", i+1, " out of ", total_iterations, " iterations")

    

# Find the indices of the best hyperparameters
best_index_linear = np.argmin(MMSE_linear)
best_C_linear = C_Values[best_index_linear]

# Training the SVM with best hyperparameters on the test set
clf_linear_best = svm.SVC(kernel='precomputed', C=best_C_linear)
clf_linear_best.fit(K_linear, y_train)
K_test_linear = linear_kernel(X_test.T, X_train.T)
y_pred_linear = clf_linear_best.predict(K_test_linear)
# test_MMSE_linear = mean_squared_error(y_test, y_pred_linear)
test_MMSE_linear = np.mean((y_test - y_pred_linear)**2)

# Print validation errors
print("Best C for Linear Kernel: ", best_C_linear)
print("Validation error for Linear Kernel: ", MMSE_linear[best_index_linear])

# Printing and plotting the results

# Generate a grid of points
x_min_plot = X_test[0, :].min() - 1
x_max_plot = X_test[0, :].max() + 1
y_min_plot = X_test[1, :].min() - 1
y_max_plot = X_test[1, :].max() + 1
x_meshgrid, y_meshgrid = np.meshgrid(np.linspace(x_min_plot, x_max_plot, 100), np.linspace(y_min_plot, y_max_plot, 100))

# Combine x_meshgrid and y_meshgrid into a single matrix
grid_points = np.c_[x_meshgrid.ravel(), y_meshgrid.ravel()]

# Compute kernel values between grid points and training data for each kernel
K_test_linear = linear_kernel(grid_points, X_train.T)

# Predict on grid points for each kernel
Z_linear = clf_linear_best.decision_function(K_test_linear)

# Reshape the decision function values
Z_linear = Z_linear.reshape(x_meshgrid.shape)

# Plot decision boundary for each kernel
plt.figure(figsize=(5, 5))
plt.scatter(X_test[0, y_test == 1], X_test[1, y_test == 1], c='blue', marker='*', label='Class 1')
plt.scatter(X_test[0, y_test == -1], X_test[1, y_test == -1], c='red', marker='*', label='Class -1')
plt.contour(x_meshgrid, y_meshgrid, Z_linear, levels=[0], linewidths=2, colors='blue')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Linear Kernel')
plt.show()
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Best C for Linear Kernel:  0.1
Validation error for Linear Kernel:  1.309090909090909
No description has been provided for this image

Polynomial Order 3 Kernel¶

In [ ]:
# Kernel Parameter
degree = 3
C_low = -5 ; C_high = 5
C_Values = np.logspace(C_low, C_high, C_high - C_low + 1, base=10)

MMSE_poly = np.zeros(len(C_Values))

# Computing kernel matrices
K_poly = polynomial_kernel(X_train.T, X_train.T, degree=degree)

# Train SVM with precomputed kernel matrices
for i, C in enumerate(C_Values):
    clf_poly = svm.SVC(kernel='precomputed', C=C)

    # Fit the model
    clf_poly.fit(K_poly, y_train)

    # Validation set
    K_val_poly = polynomial_kernel(X_Val.T, X_train.T, degree=degree)

    # Predict on validation set
    y_pred_poly = clf_poly.predict(K_val_poly)

    # Compute validation error
    # MMSE_poly[i] = mean_squared_error(y_Val, y_pred_poly)
    MMSE_poly[i] = np.mean((y_pred_poly - y_Val)**2)
    
    # % Complete status update
    print("Completed ", i+1, " out of ", total_iterations, " iterations")

# Find the indices of the best hyperparameters
best_index_poly = np.argmin(MMSE_poly)
best_C_poly = C_Values[best_index_poly]

# Training the SVM with best hyperparameters on the test set
clf_poly_best = svm.SVC(kernel='precomputed', C=best_C_poly)
clf_poly_best.fit(K_poly, y_train)
K_test_poly = polynomial_kernel(X_test.T, X_train.T, degree=degree)
y_pred_poly = clf_poly_best.predict(K_test_poly)
# test_MMSE_poly = mean_squared_error(y_test, y_pred_poly)
test_MMSE_poly = np.mean((y_test-y_pred_poly)**2)

# Print Validation errors
print("Best C for Polynomial Kernel: ", best_C_poly)
print("Validation error for Polynomial Kernel: ", test_MMSE_poly)

# Plotting the results

# Generate a grid of points
x_min_plot = X_test[0, :].min() - 1
x_max_plot = X_test[0, :].max() + 1
y_min_plot = X_test[1, :].min() - 1
y_max_plot = X_test[1, :].max() + 1
x_meshgrid, y_meshgrid = np.meshgrid(np.linspace(x_min_plot, x_max_plot, 100), np.linspace(y_min_plot, y_max_plot, 100))

# Combine x_meshgrid and y_meshgrid into a single matrix
grid_points = np.c_[x_meshgrid.ravel(), y_meshgrid.ravel()]

# Compute kernel values between grid points and training data for each kernel
K_test_poly = polynomial_kernel(grid_points, X_train.T, degree=degree)

# Predict on grid points for each kernel
Z_poly = clf_poly_best.decision_function(K_test_poly)

# Reshape the decision function values
Z_poly = Z_poly.reshape(x_meshgrid.shape)

# Plot decision boundary for each kernel
plt.figure(figsize=(5, 5))
plt.scatter(X_test[0, y_test == 1], X_test[1, y_test == 1], c='blue', marker='*', label='Class 1')
plt.scatter(X_test[0, y_test == -1], X_test[1, y_test == -1], c='red', marker='*', label='Class -1')
plt.contour(x_meshgrid, y_meshgrid, Z_poly, levels=[0], linewidths=2, colors='green')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Polynomial Kernel (Order 3)')
plt.show()
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Best C for Polynomial Kernel:  0.1
Validation error for Polynomial Kernel:  0.048
No description has been provided for this image
In [ ]:
# Kernel Parameter
degree = 3
C_low = 0.1 ; C_high = 2
C_Values = np.linspace(C_low, C_high, num=500)

MMSE_poly = np.zeros(len(C_Values))

# Computing kernel matrices
K_poly = polynomial_kernel(X_train.T, X_train.T, degree=degree)
total_iterations = len(C_Values)

# Train SVM with precomputed kernel matrices
for i, C in enumerate(C_Values):
    clf_poly = svm.SVC(kernel='precomputed', C=C)

    # Fit the model
    clf_poly.fit(K_poly, y_train)

    # Validation set
    K_val_poly = polynomial_kernel(X_Val.T, X_train.T, degree=degree)

    # Predict on validation set
    y_pred_poly = clf_poly.predict(K_val_poly)

    # Compute validation error
    # MMSE_poly[i] = mean_squared_error(y_Val, y_pred_poly)
    MMSE_poly[i] = np.mean((y_pred_poly - y_Val)**2)
    
    # % Complete status update
    print("Completed ", i+1, " out of ", total_iterations, " iterations")

# Find the indices of the best hyperparameters
best_index_poly = np.argmin(MMSE_poly)
best_C_poly = C_Values[best_index_poly]

# Training the SVM with best hyperparameters on the test set
clf_poly_best = svm.SVC(kernel='precomputed', C=best_C_poly)
clf_poly_best.fit(K_poly, y_train)
K_test_poly = polynomial_kernel(X_test.T, X_train.T, degree=degree)
y_pred_poly = clf_poly_best.predict(K_test_poly)
# test_MMSE_poly = mean_squared_error(y_test, y_pred_poly)
test_MMSE_poly = np.mean((y_test-y_pred_poly)**2)

# Print Validation errors
print("Best C for Polynomial Kernel: ", best_C_poly)
print("Validation error for Polynomial Kernel: ", test_MMSE_poly)

# Plotting the results

# Generate a grid of points
x_min_plot = X_test[0, :].min() - 1
x_max_plot = X_test[0, :].max() + 1
y_min_plot = X_test[1, :].min() - 1
y_max_plot = X_test[1, :].max() + 1
x_meshgrid, y_meshgrid = np.meshgrid(np.linspace(x_min_plot, x_max_plot, 100), np.linspace(y_min_plot, y_max_plot, 100))

# Combine x_meshgrid and y_meshgrid into a single matrix
grid_points = np.c_[x_meshgrid.ravel(), y_meshgrid.ravel()]

# Compute kernel values between grid points and training data for each kernel
K_test_poly = polynomial_kernel(grid_points, X_train.T, degree=degree)

# Predict on grid points for each kernel
Z_poly = clf_poly_best.decision_function(K_test_poly)

# Reshape the decision function values
Z_poly = Z_poly.reshape(x_meshgrid.shape)

# Plot decision boundary for each kernel
plt.figure(figsize=(5, 5))
plt.scatter(X_test[0, y_test == 1], X_test[1, y_test == 1], c='blue', marker='*', label='Class 1')
plt.scatter(X_test[0, y_test == -1], X_test[1, y_test == -1], c='red', marker='*', label='Class -1')
plt.contour(x_meshgrid, y_meshgrid, Z_poly, levels=[0], linewidths=2, colors='green')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Polynomial Kernel (Order 3)')
plt.show()
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Best C for Polynomial Kernel:  0.1
Validation error for Polynomial Kernel:  0.048
No description has been provided for this image

Radial Basis Function Kernel¶

In [ ]:
gamma_low = -5 ; gamma_high = 5
C_low = -5 ; C_high = 5

gamma_values = np.logspace(gamma_low, gamma_high, gamma_high-gamma_low+1, base=10)
C_values = np.logspace(gamma_low, gamma_high, C_high-C_low+1, base=10)

mse_values = np.zeros((len(gamma_values), len(C_values)))
total_iterations = len(gamma_values) * len(C_values)
iteration_count = 0
#Computing the kernel matrices
K_rbf = rbf_kernel(X_train.T, X_train.T)

for i, gamma in enumerate(gamma_values):
    for j, c in enumerate(C_values):
        clf_rbf = svm.SVC(kernel='precomputed', C=c)
        clf_rbf.fit(K_rbf, y_train)
        
        # Validating the model
        K_val_rbf = rbf_kernel(X_Val.T,X_train.T, gamma=gamma)

        # Predict on validation set
        Yval_Pred_rbf = clf_rbf.predict(K_val_rbf)        

        # mse_val_value = mean_squared_error(y_Val, Yval_Pred_rbf)
        mse_val_value = np.mean((y_Val - Yval_Pred_rbf)**2)
        mse_values[i, j] = mse_val_value
        
        # % Complete status update
        iteration_count += 1
        print("Completed ", iteration_count, " out of ", total_iterations, " iterations")


best_gamma_index, best_C_index = np.unravel_index(np.argmin(mse_values), mse_values.shape)
best_gamma = gamma_values[best_gamma_index]
best_C = C_values[best_C_index]
best_val_MSE = mse_values[best_gamma_index, best_C_index]

print("Best gamma: ", best_gamma)
print("Best C: ", best_C)
print(f"Best validation MSE: {best_val_MSE:.7f}")

# Training the model with the best hyperparameters on the test set
clf_rbf_best = svm.SVC(kernel='precomputed', C=best_C)
clf_rbf_best.fit(K_rbf, y_train)
K_test_rbf = rbf_kernel(X_test.T, X_train.T,gamma=best_gamma)
y_pred_rbf = clf_rbf_best.predict(K_test_rbf)
test_MMSE_rbf = np.mean((y_test - y_pred_rbf)**2)

# Generate a grid of points
x_min_plot = X_test[0, :].min() - 1
x_max_plot = X_test[0, :].max() + 1
y_min_plot = X_test[1, :].min() - 1
y_max_plot = X_test[1, :].max() + 1
x_meshgrid, y_meshgrid = np.meshgrid(np.linspace(x_min_plot, x_max_plot, 100), np.linspace(y_min_plot, y_max_plot, 100))

# Combine x_meshgrid and y_meshgri into a single matrix
grid_points = np.c_[x_meshgrid.ravel(), y_meshgrid.ravel()]

# Compute kernel values between grid points and training data for each kernel
K_test_rbf = rbf_kernel(grid_points, X_train.T, gamma=best_gamma)

# Predict on grid points for each kernel
Z_rbf = clf_rbf_best.decision_function(K_test_rbf)

# Reshape the decision function values
Z_rbf = Z_rbf.reshape(x_meshgrid.shape)

# Plot decision boundary for each kernel
plt.figure(figsize=(5, 5))
plt.contour(x_meshgrid, y_meshgrid, Z_rbf, levels=[0], linewidths=2, colors='green')
plt.scatter(X_test[0, y_test == 1], X_test[1, y_test == 1], c='blue', marker='*', label='Class 1')
plt.scatter(X_test[0, y_test == -1], X_test[1, y_test == -1], c='red', marker='*', label='Class -1')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Radial Basis Function')
plt.show()
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Best gamma:  1.0
Best C:  0.1
Best validation MSE: 0.0000000
No description has been provided for this image
In [ ]:
gamma_low = 0.5 ; gamma_high = 1.5
C_low = 0.01 ; C_high = 1

gamma_values = np.linspace(gamma_low, gamma_high, num=500)
C_values = np.linspace(gamma_low, gamma_high, num=500)

mse_values = np.zeros((len(gamma_values), len(C_values)))
total_iterations = len(gamma_values) * len(C_values)
iteration_count = 0
#Computing the kernel matrices
K_rbf = rbf_kernel(X_train.T, X_train.T)

for i, gamma in enumerate(gamma_values):
    for j, c in enumerate(C_values):
        clf_rbf = svm.SVC(kernel='precomputed', C=c)
        clf_rbf.fit(K_rbf, y_train)
        
        # Validating the model
        K_val_rbf = rbf_kernel(X_Val.T,X_train.T, gamma=gamma)

        # Predict on validation set
        Yval_Pred_rbf = clf_rbf.predict(K_val_rbf)        

        # mse_val_value = mean_squared_error(y_Val, Yval_Pred_rbf)
        mse_val_value = np.mean((y_Val - Yval_Pred_rbf)**2)
        mse_values[i, j] = mse_val_value
        
        # % Complete status update
        iteration_count += 1
        print("Completed ", iteration_count, " out of ", total_iterations, " iterations")


best_gamma_index, best_C_index = np.unravel_index(np.argmin(mse_values), mse_values.shape)
best_gamma = gamma_values[best_gamma_index]
best_C = C_values[best_C_index]
best_val_MSE = mse_values[best_gamma_index, best_C_index]

print("Best gamma: ", best_gamma)
print("Best C: ", best_C)
print(f"Best validation MSE: {best_val_MSE:.7f}")

# Training the model with the best hyperparameters on the test set
clf_rbf_best = svm.SVC(kernel='precomputed', C=best_C)
clf_rbf_best.fit(K_rbf, y_train)
K_test_rbf = rbf_kernel(X_test.T, X_train.T,gamma=best_gamma)
y_pred_rbf = clf_rbf_best.predict(K_test_rbf)
test_MMSE_rbf = np.mean((y_test - y_pred_rbf)**2)

# Generate a grid of points
x_min_plot = X_test[0, :].min() - 1
x_max_plot = X_test[0, :].max() + 1
y_min_plot = X_test[1, :].min() - 1
y_max_plot = X_test[1, :].max() + 1
x_meshgrid, y_meshgrid = np.meshgrid(np.linspace(x_min_plot, x_max_plot, 100), np.linspace(y_min_plot, y_max_plot, 100))

# Combine x_meshgrid and y_meshgri into a single matrix
grid_points = np.c_[x_meshgrid.ravel(), y_meshgrid.ravel()]

# Compute kernel values between grid points and training data for each kernel
K_test_rbf = rbf_kernel(grid_points, X_train.T, gamma=best_gamma)

# Predict on grid points for each kernel
Z_rbf = clf_rbf_best.decision_function(K_test_rbf)

# Reshape the decision function values
Z_rbf = Z_rbf.reshape(x_meshgrid.shape)

# Plot decision boundary for each kernel
plt.figure(figsize=(5, 5))
plt.contour(x_meshgrid, y_meshgrid, Z_rbf, levels=[0], linewidths=2, colors='green')
plt.scatter(X_test[0, y_test == 1], X_test[1, y_test == 1], c='blue', marker='*', label='Class 1')
plt.scatter(X_test[0, y_test == -1], X_test[1, y_test == -1], c='red', marker='*', label='Class -1')
plt.xlabel('x[n-1]')
plt.ylabel('x[n]')
plt.title('Radial Basis Function')
plt.show()
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Completed  53570  out of  250000  iterations
Completed  53571  out of  250000  iterations
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Completed  53612  out of  250000  iterations
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Completed  53621  out of  250000  iterations
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Completed  53624  out of  250000  iterations
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Completed  53627  out of  250000  iterations
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Completed  53680  out of  250000  iterations
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Completed  53711  out of  250000  iterations
Completed  53712  out of  250000  iterations
Completed  53713  out of  250000  iterations
Completed  53714  out of  250000  iterations
Completed  53715  out of  250000  iterations
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Completed  53721  out of  250000  iterations
Completed  53722  out of  250000  iterations
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Completed  53724  out of  250000  iterations
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Completed  53727  out of  250000  iterations
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Completed  53730  out of  250000  iterations
Completed  53731  out of  250000  iterations
Completed  53732  out of  250000  iterations
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Completed  53734  out of  250000  iterations
Completed  53735  out of  250000  iterations
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Completed  53740  out of  250000  iterations
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Completed  53870  out of  250000  iterations
Completed  53871  out of  250000  iterations
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Completed  195614  out of  250000  iterations
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Completed  195620  out of  250000  iterations
Completed  195621  out of  250000  iterations
Completed  195622  out of  250000  iterations
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Completed  195627  out of  250000  iterations
Completed  195628  out of  250000  iterations
Completed  195629  out of  250000  iterations
Completed  195630  out of  250000  iterations
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Completed  195635  out of  250000  iterations
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Completed  195637  out of  250000  iterations
Completed  195638  out of  250000  iterations
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Completed  195711  out of  250000  iterations
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Completed  195713  out of  250000  iterations
Completed  195714  out of  250000  iterations
Completed  195715  out of  250000  iterations
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Completed  195721  out of  250000  iterations
Completed  195722  out of  250000  iterations
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Completed  195724  out of  250000  iterations
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Completed  195727  out of  250000  iterations
Completed  195728  out of  250000  iterations
Completed  195729  out of  250000  iterations
Completed  195730  out of  250000  iterations
Completed  195731  out of  250000  iterations
Completed  195732  out of  250000  iterations
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Completed  195810  out of  250000  iterations
Completed  195811  out of  250000  iterations
Completed  195812  out of  250000  iterations
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Completed  195814  out of  250000  iterations
Completed  195815  out of  250000  iterations
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Completed  195824  out of  250000  iterations
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Completed  195827  out of  250000  iterations
Completed  195828  out of  250000  iterations
Completed  195829  out of  250000  iterations
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Completed  196710  out of  250000  iterations
Completed  196711  out of  250000  iterations
Completed  196712  out of  250000  iterations
Completed  196713  out of  250000  iterations
Completed  196714  out of  250000  iterations
Completed  196715  out of  250000  iterations
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Completed  196721  out of  250000  iterations
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Completed  196724  out of  250000  iterations
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Completed  196727  out of  250000  iterations
Completed  196728  out of  250000  iterations
Completed  196729  out of  250000  iterations
Completed  196730  out of  250000  iterations
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Completed  196735  out of  250000  iterations
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Completed  196740  out of  250000  iterations
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Completed  196821  out of  250000  iterations
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Completed  196824  out of  250000  iterations
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Completed  196827  out of  250000  iterations
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Completed  196829  out of  250000  iterations
Completed  196830  out of  250000  iterations
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Completed  196927  out of  250000  iterations
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Completed  197728  out of  250000  iterations
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Completed  197810  out of  250000  iterations
Completed  197811  out of  250000  iterations
Completed  197812  out of  250000  iterations
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Completed  197814  out of  250000  iterations
Completed  197815  out of  250000  iterations
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Completed  197820  out of  250000  iterations
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Completed  197823  out of  250000  iterations
Completed  197824  out of  250000  iterations
Completed  197825  out of  250000  iterations
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Completed  197827  out of  250000  iterations
Completed  197828  out of  250000  iterations
Completed  197829  out of  250000  iterations
Completed  197830  out of  250000  iterations
Completed  197831  out of  250000  iterations
Completed  197832  out of  250000  iterations
Completed  197833  out of  250000  iterations
Completed  197834  out of  250000  iterations
Completed  197835  out of  250000  iterations
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Completed  197837  out of  250000  iterations
Completed  197838  out of  250000  iterations
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Completed  197929  out of  250000  iterations
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Completed  197935  out of  250000  iterations
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Completed  197937  out of  250000  iterations
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Completed  197964  out of  250000  iterations
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Completed  197967  out of  250000  iterations
Completed  197968  out of  250000  iterations
Completed  197969  out of  250000  iterations
Completed  197970  out of  250000  iterations
Completed  197971  out of  250000  iterations
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Completed  197973  out of  250000  iterations
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Completed  198024  out of  250000  iterations
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Completed  198027  out of  250000  iterations
Completed  198028  out of  250000  iterations
Completed  198029  out of  250000  iterations
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Completed  198031  out of  250000  iterations
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Completed  198035  out of  250000  iterations
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Completed  198037  out of  250000  iterations
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Completed  198067  out of  250000  iterations
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Completed  198071  out of  250000  iterations
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Completed  198410  out of  250000  iterations
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Completed  198414  out of  250000  iterations
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Completed  198427  out of  250000  iterations
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Completed  198510  out of  250000  iterations
Completed  198511  out of  250000  iterations
Completed  198512  out of  250000  iterations
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Completed  198514  out of  250000  iterations
Completed  198515  out of  250000  iterations
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Completed  198520  out of  250000  iterations
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Completed  198524  out of  250000  iterations
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Completed  198527  out of  250000  iterations
Completed  198528  out of  250000  iterations
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Completed  198612  out of  250000  iterations
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Completed  198615  out of  250000  iterations
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Completed  198624  out of  250000  iterations
Completed  198625  out of  250000  iterations
Completed  198626  out of  250000  iterations
Completed  198627  out of  250000  iterations
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Completed  198924  out of  250000  iterations
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Completed  198927  out of  250000  iterations
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Completed  199022  out of  250000  iterations
Completed  199023  out of  250000  iterations
Completed  199024  out of  250000  iterations
Completed  199025  out of  250000  iterations
Completed  199026  out of  250000  iterations
Completed  199027  out of  250000  iterations
Completed  199028  out of  250000  iterations
Completed  199029  out of  250000  iterations
Completed  199030  out of  250000  iterations
Completed  199031  out of  250000  iterations
Completed  199032  out of  250000  iterations
Completed  199033  out of  250000  iterations
Completed  199034  out of  250000  iterations
Completed  199035  out of  250000  iterations
Completed  199036  out of  250000  iterations
Completed  199037  out of  250000  iterations
Completed  199038  out of  250000  iterations
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Completed  199040  out of  250000  iterations
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Completed  199060  out of  250000  iterations
Completed  199061  out of  250000  iterations
Completed  199062  out of  250000  iterations
Completed  199063  out of  250000  iterations
Completed  199064  out of  250000  iterations
Completed  199065  out of  250000  iterations
Completed  199066  out of  250000  iterations
Completed  199067  out of  250000  iterations
Completed  199068  out of  250000  iterations
Completed  199069  out of  250000  iterations
Completed  199070  out of  250000  iterations
Completed  199071  out of  250000  iterations
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Completed  199080  out of  250000  iterations
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Best gamma:  0.5
Best C:  0.5
Best validation MSE: 0.0000000
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